Results 311 to 320 of about 446,471 (361)

Finite dimensional even-quadratic functional equation and its Ulam-Hyers stability

, 2020
In this paper, we introduced m-dimensional quadratic functional equation of the form ∑1 ...
K. Tamilvanan, G. Balasubramanian, A. C. Sagayaraj   +2 more
semanticscholar   +1 more source

Quadratic variation functionals and dilation equations

Potential Analysis, 1995
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Ileana Iribarren, R. F. Gundy
openaire   +4 more sources

On approximation of approximately generalized quadratic functional equation via Lipschitz criteria

Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2018
Let G be an Abelian group with a metric d and E ba a normed space. For any f : G → E we define the generalized quadratic difference of the function f by the formula Qk f (x, y) := f (x + ky) + f (x − ky) − f (x + y) − f (x − y) − 2(k2 − 1)f (y) for all x,
Iz-iddine El-Fassi
semanticscholar   +1 more source

The quadratic function and quadratic equations

1985
The function f(x), where f(x) = ax2 + bx + c, and a, b, c are constants, a ≠ 0, is called a quadratic function, or sometimes a quadratic polynomial. From elementary algebra $${(x + d)^2} \equiv {x^2} + 2dx + {d^2}.$$ Using this, we write $$a{x^2} + bx + c \equiv a\left( {{x^2} + \frac{b}{a}x + \frac{c}{a}} \right) \equiv a\left[ {{{\left( {x
C. Plumpton, J. E. Hebborn
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Conditional equations for quadratic functions

Acta Mathematica Hungarica, 2018
We consider quadratic functions f that satisfy the additional equation y2 f(x) =  x2 f(y) for the pairs $${ (x,y) \in \mathbb{R}^2}$$ that fulfill the condition P(x, y) =  0 for some fixed polynomial P of ...
E. Garda-Mátyás, Zoltán Boros
openaire   +2 more sources

Quadratic Operators and Quadratic Functional Equation

2012
In the first part of this paper, we consider some quadratic difference operators (e.g., Lobaczewski difference operators) and quadratic-linear difference operators (d’Alembert difference operators and quadratic difference operators) in some special function spaces X λ . We present results about boundedness and find the norms of such operators.
S. Czerwik, M. Adam
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On the general quadratic functional equation [PDF]

, 2005
The author establishes the stability of the Ulam problem for the general quadratic functional equation in normed vector spaces. Let \(X\) and \(Y\) be normed vector spaces and \(Y\) be complete. A mapping \(Q: X\to Y\) is called quadratic mapping if \(Q\) satisfies \[ Q\Biggl(\sum^p_{i=1} a_i x_i\Biggr)+ \sum_{1\leq i\leq j\leq p} Q(a_j x_i- a_i x_j ...
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Quadratic Functional Equations

2009
Quadratic functional equations, bilinear forms equivalent to the quadratic equation, and some generalizations are treated in this chapter. Among the normed linear spaces (n.l.s.), inner product spaces (i.p.s.) play an important role. The interesting question when an n.l.s. is an i.p.s. led to several characterizations of i.p.s.
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Quadratic Functional Equations

2011
So far, we have discussed the stability problems of functional equations in connection with additive or linear functions. In this chapter, the Hyers–Ulam–Rassias stability of quadratic functional equations will be proved. Most mathematicians may be interested in the study of the quadratic functional equation since the quadratic functions are applied to
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Set-Valued Quadratic Functional Equations

Results in Mathematics, 2017
In this paper, we introduce set-valued quadratic functional equations and prove the Hyers–Ulam stability of the set-valued quadratic functional equations by using the fixed point method.
Choonkil Park, Jung Rye Lee, Sungsik Yun, Dong Yun Shin   +3 more
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